Formation control for cooperative containment of a diffusing substance

We present a decentralized controller to keep a group of agents at equal spacing while moving around the perimeter of a loop defined by a constant distance from a convex polygon, motivated by a cooperative containment problem. Traveling at constant speed, the agents achieve and maintain their formation by using small steering adjustments to equalize the distance between themselves and their respective leading and following neighbors. Since the formation moves around a common loop, an agent can move forward or back in formation by respectively steering slighting inside or outside the reference loop. These adjustments are controlled with the use of variable radius parameters for each agent that are shown to converge to the desired reference loop as equal spacing is achieved. We show that the proposed controller renders the desired formation locally asymptotically stable and provide simulations to demonstrate the performance of the controller for an example scenario in which the formation must recover from the loss of an agent.